Transaction Graph analysis

[Shymaa-Arafat]

I wasn't aware of this topic/research area in cryptocurrency before about a week or two; thinking about such analysis, would it help if we can predict the expected no of UTXOs, no matter how short their life is, at any given time (block no)?and hence some clues about the tree structure?
(I know that's somehow different than what u r doing, but could it help to combine both directions or view from both angles if u may say?)
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I mean if we call it T(i) for the "i"th Block, then
T(i)=T(i-1)

• SUM_forAll_TXs
  [out degree - in degree]
  .
  We can roughly say that we expect a block increase in UTXOs near to no of TXs, expecting
  T(i)~ Total no. of TXs from the start of Blockchain till Block i.
  (Note that this kind of resembles reality, since the counter says it's about 279,000 TXs per day, approximately
  2561024(256+128)*12yrs ~ 2³⁰ UTXOs nowadays)
  The exact total no of TXs as stated in
  https://www.blockchain.com/charts/n-transactions-total
  is 2³⁰ > 641.156m > 2²⁹
  .
  -While the exact total no of UTXOs is > 78m, ie 2²⁷>UTXOs>2²⁶
  -The difference maybe implies that " miners merge TXs" constitute a considerable ratio (those as described in the paper n:1 TXs where miners gather their rewards from different blocks into one address, case I in the fig.)
  

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So if we can analyze this SUM further into different TXs categories, for example a miner coinbase tx has no "in", stock, hot/cold wallet, DEX,...
to get some insight about arranging them in a tree/forest.
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Maybe this seems trivial or straight forward, but I didn't see it anywhere?
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The paper that started those thoughts is
Bitcoin_tcm18-302979.pdf
"Do Bitcoin Users Really Care About Anonymity?
An Analysis of the Bitcoin Transaction Graph", Anil Gaihre, Yan Luo, Hang Liu, University of Massachusetts Lowell.
last ref in it is 15/8/2018

[Shymaa-Arafat]

I should add to this that..
It seems this is not the only or standard graph representation, in
https://appliednetsci.springeropen.com/articles/10.1007/s41109-019-0249-6#ref-CR9
They used a different mapping ...

In the transaction graph of a cryptocurrency, vertices are accounts (or addresses) in the currency network, and the edges between them are transactions between those accounts.

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It's also said that it follows the Power law distribution, as u said in ur paper about UTXOs life span?

We also found that the transaction graph of these currencies is non-assortative, i.e. addresses do not tend for transact with a particular type of addresses of higher or lower degree, and the degree sequence of their transaction graph follows the power law distribution.

So, there is a real correspondence here; maybe I just can't like put my hands on the best use of it, yet.